An important characteristic of bosons is that there is no restriction on the number of them that occupy the same quantum state. This property is exemplified by helium-4 when it is cooled to become a superfluid.[10] Unlike bosons, two identical fermions cannot occupy the same quantum state. Whereas the elementary particles that make up matter (i.e. leptons and quarks) are fermions, the elementary bosons are force carriers that function as the 'glue' holding matter together.[11] This property holds for all particles with integer spin (s = 0, 1, 2, etc.) as a consequence of the spin–statistics theorem.
When a gas of Bose particles is cooled down to temperatures very close to absolute zero, then the kinetic energy of the particles decreases to a negligible amount, and they condense into the lowest energy level state. This state is called a Bose–Einstein condensate. This property is also the explanation for superfluidity.

There may be a sixth tensor boson (spin=2), the graviton (G), that would be the force-carrier for gravity. It remains a hypothetical elementary particle since all attempts so far to incorporate gravitation into the Standard Model have failed. If the graviton does exist, it must be a boson, and could conceivably be a gauge boson.[b]

Properties

Symmetric wavefunction for a (bosonic) 2-particle state in an infinite square well potential.

Bosons differ from fermions, which obey Fermi–Dirac statistics. Two or more identical fermions cannot occupy the same quantum state (see Pauli exclusion principle), and they are sometimes said to be the constituents of ordinary "rigid" matter. Unlike those, instances of a boson have no quantum-mechanical obstruction to occupy the same state. Bosons are often (although not necessarily) force carrier particles, including composite bosons such as mesons. Force carriers are also said to be the particles that transmit interactions, or the constituents of radiation.

All known elementary and composite particles are bosons or fermions, depending on their spin: Particles with half-integer spin are fermions; particles with integer spin are bosons. In the framework of nonrelativistic quantum mechanics, this is a purely empirical observation. In relativistic quantum field theory, the spin–statistics theorem shows that half-integer spin particles cannot be bosons and integer spin particles cannot be fermions.[13]

In large systems, the difference between bosonic and fermionic statistics is only apparent at large densities — when their wave functions overlap. At low densities, both types of statistics are well approximated by Maxwell–Boltzmann statistics, which is described by classical mechanics.

Composite bosons

Composite particles (such as hadrons, nuclei, and atoms) can be bosons or fermions depending on their constituents. More precisely, because of the relation between spin and statistics, a particle containing an even number of fermions is a boson, since it has integer spin.

The number of bosons within a composite particle made up of simple particles bound with a potential has no effect on whether it is a boson or a fermion.

Quantum states

Bose–Einstein statistics encourages identical bosons to crowd into one quantum state, but not any state is necessarily convenient for it. Aside of statistics, bosons can interact – for example, helium-4 atoms are repulsed by intermolecular force on a very close approach, and if one hypothesizes their condensation in a spatially-localized state, then gains from the statistics cannot overcome a prohibitive force potential. A spatially-delocalized state (i.e. with low |ψ(x)|) is preferable: if the number density of the condensate is about the same as in ordinary liquid or solid state, then the repulsive potential for the N-particle condensate in such state can be no higher than for a liquid or a crystalline lattice of the same N particles described without quantum statistics. Thus, Bose–Einstein statistics for a material particle is not a mechanism to bypass physical restrictions on the density of the corresponding substance, and superfluid liquid helium has a density comparable to the density of ordinary liquid matter. Spatially-delocalized states also permit for a low momentum according to the uncertainty principle, hence for low kinetic energy; this is why superfluidity and superconductivity are usually observed in low temperatures.

Photons do not interact with themselves and hence do not experience this difference in states where to crowd (see squeezed coherent state).

References

^Carroll, Sean (2007). Guidebook. Dark Matter, Dark Energy: The dark side of the universe. The Teaching Company. Part 2, p. 43. ISBN978-1598033502. ... boson: A force-carrying particle, as opposed to a matter particle (fermion). Bosons can be piled on top of each other without limit. Examples are photons, gluons, gravitons, weak bosons, and the Higgs boson. The spin of a boson is always an integer: 0, 1, 2, and so on ...